Preheat the oven to 350°F and spray a 9x5-inch loaf pan with non-stick spray.
Rinse the zucchini and trim off the ends. Use a fine grater to shred the zucchini. Gently wrap the shredded zucchini in a clean towel and squeeze out any excess water. Set aside.
In a medium bowl whisk together the flour, baking soda, baking powder, cinnamon, and salt.
To a large bowl, add the bananas. Use a fork to mash. Add in the sugar, eggs, oil, and vanilla. Stir until fully combined.
Add the flour mixture, and stir until just combined.
Add in the grated zucchini and stir until incorporated.
Pour into the prepared pan.
Bake until a toothpick comes out clean, about 70-80 minutes, checking the bread at 70 minutes. The outside will be dark brown and an inserted toothpick should be removed with crumbs, but not wet batter. If the loaf is getting too dark, you can add an aluminum foil tent for the last 10-15 minutes.
Let the bread cool slightly before cutting and serving.